Steady-state vibrations of an elastic system in combination parametric resonance

1972 ◽  
Vol 8 (2) ◽  
pp. 120-124
Author(s):  
Yu. V. Osetinskii
Keyword(s):  
Steady State ◽  
Parametric Resonance ◽  
Elastic System ◽  
Combination Parametric Resonance

Principal parametric resonance of axially accelerating viscoelastic strings with an integral constitutive law

2005 ◽  
Vol 461 (2061) ◽  
pp. 2701-2720 ◽  
Author(s):  
Li-Qun Chen
Keyword(s):  
Steady State ◽  
Parametric Resonance ◽  
Multiple Scales ◽  
Constitutive Law ◽  
Transverse Motion ◽  
Viscoelastic Parameters ◽  
Principal Parametric Resonance ◽  
Linearized Stability ◽  
Speed Fluctuation ◽  
Axial Speed

The steady-state transverse responses and the stability of an axially accelerating viscoelastic string are investigated. The governing equation is derived from the Eulerian equation of motion of a continuum, which leads to the Mote model for transverse motion. The Kirchhoff model is derived from the Mote model by replacing the tension with the averaged tension over the string. The method of multiple scales is applied to the two models in the case of principal parametric resonance. Closed-form expressions of the amplitudes and the existence conditions of steady-state periodical responses are presented. The Lyapunov linearized stability theory is employed to demonstrate that the first (second) non-trivial steady-state response is always stable (unstable). Numerical calculations show that the two models are qualitatively the same, but quantitatively different. Numerical results are also presented to highlight the effects of the mean axial speed, the axial-speed fluctuation amplitude, and the viscoelastic parameters.

scholarly journals Unusual Combination Parametric Resonance

2014 ◽  
Vol 91 ◽  
pp. 154-159
Author(s):  
Zbigniew Wójcicki ◽  
Danuta Bryja
Keyword(s):  
Parametric Resonance ◽  
Unusual Combination ◽  
Combination Parametric Resonance

Principal Parametric Resonance of Axially Accelerating Viscoelastic Strings

2005 ◽  
Author(s):  
Li-Qun Chen
Keyword(s):  
Steady State ◽  
Parametric Resonance ◽  
Multiple Scales ◽  
Transverse Motion ◽  
Viscoelastic Parameters ◽  
Principal Parametric Resonance ◽  
Linearized Stability ◽  
Speed Fluctuation ◽  
The Stability ◽  
Axial Speed

The steady-state transverse responses and the stability of an axially accelerating viscoelastic string are investigated. The governing equation is derived from the Eulerian equation of motion of a continuum, which leads to the Mote model for transverse motion. The Kirchhoff model is derived from the Mote model by replacing the tension with the averaged tension over the string. The method of multiple scales is applied to the two models in the case of principal parametric resonance. Closed-form expressions of the amplitudes and the existence conditions of steady-state periodical responses are presented. The Lyapunov linearized stability theory is employed to demonstrate that the first (second) nontrivial steady-state response is always stable (unstable). Numerical calculations show that the two models are qualitatively the same, but quantitatively different. Numerical results are also presented to highlight the effects of the mean axial speed, the axial speed fluctuation amplitude, and the viscoelastic parameters.

Difference combination parametric resonance; Application to the garden hose problem

SeMA Journal ◽  
2010 ◽  
Vol 51 (1) ◽  
pp. 63-70 ◽  
Author(s):  
Jorge Galán Vioque ◽  
A. R. Champneys ◽  
M. Truman
Keyword(s):  
Parametric Resonance ◽  
Combination Parametric Resonance

scholarly journals Polariton condensation, superradiance and difference combination parametric resonance in mode-locked laser

2017 ◽  
Vol 917 ◽  
pp. 062028
Author(s):  
S N Bagayev ◽  
R M Arkhipov ◽  
M V Arkhipov ◽  
V S Egorov ◽  
I A Chekhonin ◽  
...  
Keyword(s):  
Parametric Resonance ◽  
Mode Locked Laser ◽  
Combination Parametric Resonance

Parametric Excitation of a Pendulum With Bilinear Hysteresis

1970 ◽  
Vol 37 (4) ◽  
pp. 1061-1068 ◽  
Author(s):  
W. K. Tso ◽  
K. G. Asmis
Keyword(s):  
Steady State ◽  
Parametric Resonance ◽  
Parametric Excitation ◽  
Viscous Damping ◽  
Sinusoidal Oscillation ◽  
Effective Mechanism ◽  
Steady State Responses ◽  
The Stability ◽  
State Responses ◽  
Steady State Solutions

The steady-state responses of a simple pendulum with a hinge exhibiting bilinear hysteretic moment-rotation characteristics and parametrically excited by a sinusoidal oscillation at the base is given. The stability of the steady-state solutions is discussed. It is shown that in contrast with viscous damping, the bilinear hysteresis is an effective mechanism to limit the growth of the response during parametric resonance.

scholarly journals Излучение резонансной среды, возбуждаемое лазерным излучением с периодической фазовой модуляцией в режиме сильной связи поля и вещества

2019 ◽  
Vol 127 (12) ◽  
pp. 967
Author(s):  
Р.М. Архипов ◽  
М.В. Архипов ◽  
В.С. Егоров ◽  
И.А. Чехонин ◽  
М.А. Чехонин ◽  
...  
Keyword(s):  
Laser Radiation ◽  
Laser Pulse ◽  
Parametric Resonance ◽  
Frequency Modulation ◽  
Carrier Frequency ◽  
Phase Modulation ◽  
Resonant Medium ◽  
High Excitation ◽  
Effective Excitation ◽  
Combination Parametric Resonance

In this paper, the radiation of a two-level resonant medium placed in a cavity and excited by a laser pulse with periodic phase modulation is studied theoretically. The analysis is carried out on the basis of an analytical and numerical solution of the system of Maxwell-Bloch equations under conditions when the regime of strong coupling of the field and matter is realized. Under these conditions, this system is similar to a polariton laser. A high excitation efficiency of a polariton laser by a phase-modulated radiation pulse compared with a pulse without phase modulation of the carrier frequency is shown. It is shown that the main reason for the effective excitation of polariton modes of the medium is the occurrence of a difference combination parametric resonance. The results obtained open up new possibilities in the excitation of radiation from polariton lasers by low-power pumping laser radiation with frequency modulation.

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